def test_dpi(self):
np.random.seed(0)
for _ in range(10):
zero_dim = np.random.randint(1, 10)
pos_dim = np.random.randint(1, 10)
soc_dim = [
np.random.randint(1, 10)
for _ in range(np.random.randint(1, 10))
]
psd_dim = [
np.random.randint(1, 10)
for _ in range(np.random.randint(1, 10))
]
exp_dim = np.random.randint(3, 18)
cones = [(cone_lib.ZERO, zero_dim), (cone_lib.POS, pos_dim),
(cone_lib.SOC, soc_dim), (cone_lib.PSD, psd_dim),
(cone_lib.EXP, exp_dim), (cone_lib.EXP_DUAL, exp_dim)]
size = zero_dim + pos_dim + sum(soc_dim) + sum(
[cone_lib.vec_psd_dim(d) for d in psd_dim]) + 2 * 3 * exp_dim
x = np.random.randn(size)
for dual in [False, True]:
cone_list_cpp = cone_lib.parse_cone_dict_cpp(cones)
proj_x = cone_lib.pi(x, cones, dual=dual)
dx = 1e-7 * np.random.randn(size)
z = cone_lib.pi(x + dx, cones, dual=dual)
Dpi = _diffcp.dprojection(x, cone_list_cpp, dual)
np.testing.assert_allclose(Dpi.matvec(dx),
z - proj_x,
atol=1e-6)
Dpi = _diffcp.dprojection_dense(x, cone_list_cpp, dual)
np.testing.assert_allclose(Dpi @ dx, z - proj_x, atol=1e-6)
def test_dpi(self):
for _ in range(10):
zero_dim = np.random.randint(1, 10)
pos_dim = np.random.randint(1, 10)
soc_dim = [
np.random.randint(1, 10)
for _ in range(np.random.randint(1, 10))
]
psd_dim = [
np.random.randint(1, 10)
for _ in range(np.random.randint(1, 10))
]
exp_dim = np.random.randint(3, 18)
exp_dim -= (exp_dim % 3)
cones = [(cone_lib.ZERO, zero_dim), (cone_lib.POS, pos_dim),
(cone_lib.SOC, soc_dim), (cone_lib.PSD, psd_dim),
(cone_lib.EXP, exp_dim)]
size = zero_dim + pos_dim + sum(soc_dim) + sum(
[cone_lib.vec_psd_dim(d) for d in psd_dim]) + exp_dim
x = np.random.randn(size)
for dual in [False, True]:
Dpi = cone_lib.dpi(x, cones, dual=dual)
proj_x = cone_lib.pi(x, cones, dual=dual)
dx = 1e-6 * np.random.randn(size)
z = cone_lib.pi(x + dx, cones, dual=dual)
np.testing.assert_allclose(Dpi @ dx,
z - proj_x,
atol=1e-3,
rtol=1e-4)
def test_ecos_solve(self):
np.random.seed(0)
m = 20
n = 10
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
cone_dims.pop("q")
cone_dims.pop("s")
cone_dims.pop("ep")
x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
A, b, c, cone_dims, solve_method="ECOS")
# check optimality conditions
np.testing.assert_allclose(A @ x + s, b, atol=1e-8)
np.testing.assert_allclose(A.T @ y + c, 0, atol=1e-8)
np.testing.assert_allclose(s @ y, 0, atol=1e-8)
np.testing.assert_allclose(s,
cone_lib.pi(
s,
cone_lib.parse_cone_dict(cone_dims),
dual=False),
atol=1e-8)
np.testing.assert_allclose(y,
cone_lib.pi(
y,
cone_lib.parse_cone_dict(cone_dims),
dual=True),
atol=1e-8)
x = cp.Variable(10)
prob = cp.Problem(
cp.Minimize(
cp.sum_squares(np.random.randn(5, 10) @ x) +
np.random.randn(10) @ x), [
cp.norm2(x) <= 1,
np.random.randn(2, 10) @ x == np.random.randn(2)
])
A, b, c, cone_dims = utils.scs_data_from_cvxpy_problem(prob)
x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
A, b, c, cone_dims, solve_method="ECOS")
# check optimality conditions
np.testing.assert_allclose(A @ x + s, b, atol=1e-8)
np.testing.assert_allclose(A.T @ y + c, 0, atol=1e-8)
np.testing.assert_allclose(s @ y, 0, atol=1e-8)
np.testing.assert_allclose(s,
cone_lib.pi(
s,
cone_lib.parse_cone_dict(cone_dims),
dual=False),
atol=1e-8)
np.testing.assert_allclose(y,
cone_lib.pi(
y,
cone_lib.parse_cone_dict(cone_dims),
dual=True),
atol=1e-8)
def pi(z, cones):
"""Projection onto R^n x K^* x R_+
`cones` represents a convex cone K, and K^* is its dual cone.
"""
u, v, w = z
return np.concatenate(
[u, cone_lib.pi(v, cones, dual=True),
np.maximum(w, 0)])
def test_pi(self):
for _ in range(10):
zero_dim = np.random.randint(1, 10)
pos_dim = np.random.randint(1, 10)
soc_dim = [
np.random.randint(1, 10)
for _ in range(np.random.randint(1, 10))
]
psd_dim = [
np.random.randint(1, 10)
for _ in range(np.random.randint(1, 10))
]
exp_dim = np.random.randint(3, 18)
exp_dim -= (exp_dim % 3)
cones = [(cone_lib.ZERO, zero_dim), (cone_lib.POS, pos_dim),
(cone_lib.SOC, soc_dim), (cone_lib.PSD, psd_dim),
(cone_lib.EXP, exp_dim)]
size = zero_dim + pos_dim + sum(soc_dim) + sum(
[cone_lib.vec_psd_dim(d) for d in psd_dim]) + exp_dim
x = np.random.randn(size)
for dual in [False, True]:
proj = cone_lib.pi(x, cones, dual=dual)
offset = 0
np.testing.assert_allclose(
proj[:zero_dim],
cone_lib._proj(x[:zero_dim], cone_lib.ZERO, dual=dual))
offset += zero_dim
np.testing.assert_allclose(
proj[offset:offset + pos_dim],
cone_lib._proj(x[offset:offset + pos_dim],
cone_lib.POS,
dual=dual))
offset += pos_dim
for dim in soc_dim:
np.testing.assert_allclose(
proj[offset:offset + dim],
cone_lib._proj(x[offset:offset + dim],
cone_lib.SOC,
dual=dual))
offset += dim
for dim in psd_dim:
dim = cone_lib.vec_psd_dim(dim)
np.testing.assert_allclose(
proj[offset:offset + dim],
cone_lib._proj(x[offset:offset + dim],
cone_lib.PSD,
dual=dual))
offset += dim
np.testing.assert_allclose(
proj[offset:],
cone_lib._proj(x[offset:], cone_lib.EXP, dual=dual))